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Modular multilevel cascade converter (MMCC) is a family of the emerging multilevel converters that are configured with a cascaded connection of full-bridge submodules or half-bridge ones by distinct topological structures. So far, MMCC family can be classified by basic configurations and submodule types into single-star full-bridge, double-star half-bridge (modular multilevel converter (MMC)), double-star full-bridge, double-star half-bridge back-to-back (indirect MMC), triplestar full-bridge (modular multilevel matrix converter, M3C), single-delta full-bridge and double-delta full-bridge (Hexverter). This study introduces a generalised and standard analytical procedure for MMCC and deals with the double-star half-bridge case (MMC) as example. A particular defined circulating current with a clearer physical meaning is used to analyse the complicated branch current composition and branch energy fluctuation. A full mathematical model based on state-space equations is established for MMC and a corresponding energy-current control strategy is presented. The validity of the control design and effectiveness of MMC is confirmed by simulation and experiment.